is satisfied. We require that \(W\)  satisfy the assumptions in REF . This is necessary for us to introduce a generalized notion of the determinant of \(\Lambda \) . The necessary and sufficient condition, for the existence of \(U \in \mathcal {D}^{\prime }(\Omega ,\mathbb {R}^2)\)  satisfying (REF )\(_1\) , then follows from [1]} as
\(\operatorname{Curl}\operatorname{Curl}E + \operatorname{Det}(\Lambda )=0,\) 
